Report on Discrete Mathematics

Running head: REPORT ON DISCRETE MATHEMATICS
REPORT
ON
DISCRETE MATHEMATICS
Name of the Student
Name of the University
Author Note:

DISCRETE MATHEMATICS1
Statement: Prove that the sum of the first n natural numbers is,
0+1+ ...+n=n( n+1
2 )
Proof:
If n = 0, Left Hand Side (LHS) = 0, Right Hand Side (RHS) = 0 × (0+1) = 0.
Hence, it is proved that LHS = RHS.
As per the mathematical induction- It is assumed that for n, as an arbitrary natural number the
induction hypothesis is,0+1+ ...+n=n( n+1
2 ).
While proving it for n+1, the LHS will be n+1, where the entire expression will be, n +
1 = 0 + 1 + ... + n + (n + 1) = (0 + 1 + ... + n) + (n + 1) for the LHS (n+1)
If we factor the (n +1) from the expression, we will get
(n +1)(n+2)/2..............................equal to the RHS for (n+1)
Hence, LHS = RHS of (n+1)...... (Proved)